reserve z1,z2,z3,z4,z for Quaternion;

theorem
  <k>^3=-<k>
proof
 <k>*<k>*<k> = ([* 0*0-0*0-0*0-1*1, 0*0+0*0+0*1-1*0, 0*0+0*0+0*1-1*0, 0*1
  +1*0+0*0-0*0 *])*[*0,0,0,jj*] by QUATERNI:def 10
    .= [* (-1)*0-0*0-0*0-0*1,(-1)*0+0*0+0*1-0*0, (-1)*0+0*0+0*0-1*0,(-1)*1+0
  *0+0*0-0*0 *] by QUATERNI:def 10
    .=-[*0,0,0,jj*] by QUATERN2:4;
  hence thesis;
end;
